A fuzzy case based reasoning approach to value engineering

doi:10.1016/j.eswa.2011.01.124

Expert Systems with Applications

Volume 38, Issue 8, August 2011, Pages 9334-9339

https://doi.org/10.1016/j.eswa.2011.01.124 Get rights and content

Abstract

This paper is intended to assist the experts during the creativity phase of value engineering through utilizing the past experiences and avoid them in a specific domain from repeating the same experience. To this purpose, a general fuzzy case based reasoning (CBR) system is developed. Our system benefits from a fuzzy clustering model for fuzzy data to facilitate case retrieval and reduce the time complexity. The inherent analogical nature of a case-based reasoning (CBR) model and its integration with fuzzy theory would facilitate access to more precise and systematically classified information during a VE workshop. In order to test the performance of the proposed system, it is applied to suburban highway design data extracted from National Cooperative Highway Research Program (NCHRP) Report 282.

Research highlights

► A fuzzy case based reasoning system for value engineering is developed. ► Our system benefits from a fuzzy clustering model for fuzzy data. ► The performance of our system is tested with suburban highway design data.

Introduction

Value engineering (VE) is an organized approach directed at analyzing the function of systems, facilities, services, and supplies for the purpose of achieving their essential functions at the lowest life-cycle cost consistent with required performance, reliability, quality and safety (Mandelbaum & Reed, 2006). The VE process consists of several phases, including the information phase, function analysis phase, creativity phase, evaluation phase, presentation phase and implementation phase. Creativity depends on the human brain and cannot be computerized easily by conventional programming. Case-based reasoning (CBR) from AI can be used to improve efficiency of this stage, since this approach is able to utilize the specific knowledge of experiences by retrieving and adapting the solutions from similar past cases.

In the literature, existing models mainly involve conventional approaches and less has been devoted to devising AI approaches. One of the earliest works was done by the US Army Corps of Engineers through establishing an information retrieval system called VE-trieval. This program can be queried by key-word methodology on a particular subject to obtain an abstract and other useful information (Degenhardt, 1985). Park (1994) developed VEPRO which is a spreadsheet rule-based system with database features and consists of several models parallel to the VE job plan. Alcantara (1996) designed a support program for the information phase of VE, which assigned data structure for representing and performing analytical tasks on rational data. A computer model for VE methodology was developed by Assaf, Jannadi, and Al-Tamimi (2000) emphasizing life cycle cost calculations. Dahim (2001) at Pittsburgh University developed an expert system for VE application in suburban highway design. It utilizes the analytical hierarchy process (AHP) method for the evaluation phase of VE. Naderpajouh and Afshar (2008) proposed a conceptual expert case-based reasoning (CBR) framework that outlines knowledge entities and their relations in the VE workshop. It also benefits from a fuzzy approach to handle uncertainties in the evaluation phase of the job plan. In general, devising an expert system for a VE job plan is recommended by different researches (Al-Yousefi, 1991, Assaf et al., 2000, Shen and Brandon, 1991).

The main objective of this study is to assist the experts during the creativity phase of VE through utilizing the past experiences to prevent repeating the same experience in a particular domain. To this purpose, a comprehensive fuzzy CBR system is proposed involving fuzzy representation of cases and a fuzzy clustering of fuzzy data model to similarity matching in order to facilitate case retrieval. The basic idea that motivates us to use fuzzy theory is that in early stages of the project development, where VE has the greatest payoffs (Dell’Isola, 1998), most of the parameters have uncertainties (Naderpajouh, Afshar, & Mirmohammadsadeghi, 2006). In addition, many experts cannot express their judgments in accurate numerical terms and use linguistic expressions. In these cases, fuzzy theory may be employed to handle uncertainties and support linguistic assessments. Thus, the inherent analogical nature of a case-based reasoning (CBR) model and its integration with fuzzy theory would facilitate access to more precise and systematically classified information during a VE workshop.

The rest of the paper is organized as follows. Section 2 summarizes the literature survey for the related areas. We propose a distance measure for fuzzy data based on Wasserstein Metric in Section 3; by means of this distance and following Keller’s approach, we propose a fuzzy clustering model for fuzzy data with outliers (Section 4). For determining the optimal number of clusters, we modify Kown (1998) validity index so that it can be used in a complete fuzzy framework and also in noisy environments (Section 5). In Section 6, the main methodology is proposed. As an application, our system is tested on suburban highway design data provided in NCHRP Report 282 (NCHRP, 1986). Finally, conclusions and future works are presented in Section 8.

Section snippets

Background

This section will briefly provide some relative literature in the areas of case-based reasoning, fuzzy case-based reasoning, clustering analysis, fuzzy data and Metrics for fuzzy data.

The proposed distance for fuzzy data

In this section, we first present a new distance measure for interval-valued data, and then it is used to formulate the distance measure for fuzzy data.

Let I_i = [a_i,b_i], be an interval for $i = 1, 2$ . We can parameterize I_i as follows: $I_{i} (t) = a_{i} + t (b_{i} - a_{i}) 0 ⩽ t ⩽ 1 .$ If we represent I_i by means of its midpoint $m_{i} = \frac{a_{i} + b_{i}}{2}$ and radius $δ_{i} = \frac{b_{i} - a_{i}}{2}$ , Eq. (9) can be rewritten as follows: $I_{i} (t) = m_{i} + (2 t - 1) δ_{i} 0 ⩽ t ⩽ 1 .$ The distance measure between I₁ and I₂ can be defined as follows: $d^{2} (I_{1}, I_{2}) = \int_{0}^{1} [I_{1} (t) - I_{2} (t)]^{2} dt = \int_{0}^{1} [(m_{1} - m_{2}) + (δ_{1} - δ_{2})$

Fuzzy clustering of fuzzy data with outliers

In this section Keller’s approach (Keller, 2000) is modified so that it can be used for fuzzy data. Similar to his approach, an additional weighting factor is added for each datum to identify outliers and reduce their effects. Before describe the procedure, let us introduce the following notation:

U ≡ {u_ik:i = 1, …, c;k = 1, …, n} is the membership matrix of order (c × n), where c is the number of clusters, n is the number of data vectors; u_ik ∈ [0, 1] denotes the membership degree of the kth object to the ith

Cluster validity index

As Pal and Bezdek (1995) pointed out, once clusters are found, it is necessary to validate them. This is a cluster validity problem. In the literature, we can find many validity indices. Early indices such as partition coefficient and partition entropy (Bezdek, 1974a, Bezdek, 1974b) can be directly applied to the fuzzy clustering of fuzzy data, but they use only fuzzy memberships, which may not have close connection to the geometrical structure of data, (Zhang, Wang, Zhang, & Li, 2008). There

Methodology

This section presents the methodology of developing our system and presents its modules in detail.

Application

Our system was tested on suburban highway design data which was extracted from the National Cooperative Highway Research Program (NCHRP) Report 282 (NCHRP, 1986). The features include existing design, maximum available width and the desirability of operational and safety indices. The existing design can be one of these options:

•
Two-lane Undivided, abbreviated as 2U.
•
Three-Lane Divided with Center Two-Way- Left-Turn Lane, abbreviated as 3T.
•
Four-Lane Undivided, abbreviated as 4U.
•
Four-Lane Divided

Conclusion and future works

This paper presented a fuzzy CBR system for value engineering. This system can contribute significantly to the efficiency of the value study, providing the VE team with an extensive memory of previous experiences. Since cases are fuzzy data, a fuzzy clustering model for fuzzy data, based on a new distance is used to reduce the cases necessary for searching and save time. In addition, Kwon cluster validity index is modified to validate the number of clusters. Finally, to test the performance of

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